Fixed-point iteration, Exercise 2

$$g(x) = 1 + x - \frac 19 x^2, p = 3$$

g2(x) = 1 + x - (1/9)*x^2;

x2 = [0.0];

for k = 1:25
  push!(x2,g2(x2[k]))
end

err = @. abs(x2 - 3);

plot(0:25, err, m =:o,
     yaxis = ("error", :log10))

y2 = log.(err[18:25]);
p = Polynomials.fit(18:25, y2, 1);
sigma = exp(p.coeffs[2])